INFLUENCE OF RIGID BOUNDARY ON THE LOVE WAVE PROPAGATION IN ELASTIC LAYER WITH VOID PORES

In this paper, a mathematical model for Love wave propagation in a porous elastic layer under a rigid boundary resting over a poro-elastic half-space has been developed. The study shows that such a medium transmits two types of Love waves. The first front depends on the change in volume fraction of the pores whereas the second front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the Love wave in an elastic layer over an elastic half-space. It is observed that the first front is many times faster than the shear wave in the medium with void pores due to the change in the volume fraction of the pores and is significant.     

Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space

In the present paper we study the effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a semi-infinite heterogeneous half-space, where the heterogeneity is both in rigidity and density. The present study demonstrates that torsional waves can propagate in the layer. The velocities of torsional waves have been calculated numerically as a functions of KH, (where K is the wave number and H is the thickness of the layer) and are presented in a number of graphs. It is also observed that, for a layer over a homogeneous half-space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary whereas it does at the free boundary.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

梯度半空间梯度覆层中的Love波

对功能梯度弹性半空间上覆盖一层功能梯度材料中的Love波的频散问题进行了研究，给出 了Love波频散方程的一般形式. 对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运 动控制方程进行了求解，给出了半空间和覆盖层的位移、应力解析解，给出了Love波在该解析 解下的频散方程. 以覆盖层的剪切弹性模量和质量密度均呈指数函数变化，半空间的剪切弹 性模量和质量密度均呈抛物线变化为例，利用迭代方法对频散方程进行了求解，给出了频散 曲线. 结果显示：在最低阶振型频散曲线中出现截止频率.     

A Linear Theory of Porous Elastic Solids

The theory of porous elastic solids with large vacuous interstices, considered by Giovine like materials with ellipsoidal structure, includes, as a particular case, the nonlinear theory of Nunziato and Cowin of elastic materials with small spherical voids finely dispersed in the matrix.In this paper we propose appropriate constitutive relations and then specialize the basic balance equations of Giovine to the linear theory. Also, generalizing the developments of Cowin and Nunziato, we formulate boundary-initial-value problems and examine classical applications as responses to homogeneous deformations and small-amplitude acoustic waves.     

Love wave dispersion in pre-stressed homogeneous medium over a porous half-space with irregular boundary surfaces

The paper investigates the existence of Love wave propagation in an initially stressed homogeneous layer over a porous half-space with irregular boundary surfaces. The method of separation of variables has been adopted to get an analytical solution for the dispersion equation and thus dispersion equations have been obtained in several particular cases. Propagation of Love wave is influenced by initial stress parameters, corrugation parameter and porosity of half-space. Velocity of Love waves have been plotted in several figures to study the effect of various parameters and found that the velocity of wave decreases with increases of non-dimensional wave number. It has been observed that the phase velocity decreases with increase of initial stress parameters and porosity of half-space.     

Decaying surface waves in inhomogeneous media

Two problems on plane decaying surface waves in an inhomogeneous medium are under consideration: the problem where the waves similar to Rayleigh waves propagate in an isotropic elastic half-space that borders with a layer of an ideal incompressible fluid and the problem where the waves similar to Love waves propagate in a semi-infinite saturated porous medium that borders with a layer of an isotropic elastic medium.     

Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson’s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.     

Finite-amplitude Love waves in a pre-stressed compressible elastic half-space with a double surface layer

The dispersive behavior of finite-amplitude time-harmonic Love waves propagating in a pre-stressed compressible elastic half-space overlaid with two compressible elastic surface layers of finite thickness is investigated. The half-space and layers are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. Results for the energy density and energy flux of the waves are also presented. The special case where the interfaces between the layers and the half-space are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the Love wave speed with the pre-stress and the propagation angle.     

Destabilization of long-wavelength Love and Stoneley waves in slow sliding

Love waves are dispersive interfacial waves that are a mode of response for anti-plane motions of an elastic layer bonded to an elastic half-space. Similarly, Stoneley waves are interfacial waves in bonded contact of dissimilar elastic half-spaces, when the displacements are in the plane of the solids. It is shown that in slow sliding, long-wavelength Love and Stoneley waves are destabilized by friction. Friction is assumed to have a positive instantaneous logarithmic dependence on slip rate and a logarithmic rate weakening behavior at steady-state.Long-wavelength instabilities occur generically in sliding with rate- and state-dependent friction, even when an interfacial wave does not exist. For slip at low rates, such instabilities are quasi-static in nature, i.e., the phase velocity is negligibly small in comparison to a shear wave speed. The existence of an interfacial wave in bonded contact permits an instability to propagate with a speed of the order of a shear wave speed even in slow sliding, indicating that the quasi-static approximation is not valid in such problems.     

Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress

The present work deals with the possibility of propagation of torsional surface wave in fluid saturated poroelastic layer lying over nonhomogeneous elastic half space. Both the media are assumed to be under compressive initial stress. The half space has two types of inhomogeneity, viz; hyperbolic and quadratic. The dispersion equation for torsional wave in porous layer has been derived and observed that the presence of fluid in pores increases the velocity of the torsional surface wave but the phase velocity diminishes due to the presence of compressive initial stress in the porous layer. It is also observed that the velocity of the torsional surface wave increases due to the increase of initial stress in inhomogeneous half space. The inhomogeneity factor due to quadratic and hyperbolic variations in rigidity, density and initial stress of the medium decreases the phase velocity as it increases.     

Note on the propagation of love waves in a half-space with an elastic triple superficial layer subject to a high two-dimensional stress

The propagation of Love waves is investigated involving a triple superficial layer on a half-space, the entire system being elastic and highly stressed in two horizontal directions. The non-linear problem is illustrated numerically. A graph displays the phase velocity dependence on the wave length.     

Effect of loosely bonded undulated boundary surfaces of doubly layered half-space on the propagation of torsional wave

This paper investigates the propagation of torsional wave in an initially stressed poroelastic layer with corrugated as well as loosely bonded boundary surfaces, sandwiched between a corrugated fiber-reinforced layer and a viscoelastic half-space under initial stress. The velocity equation has been obtained in closed form analytically and the substantial effect of affecting parameters on the phase velocity of torsional surface wave has been demonstrated numerically and graphically. Comparative study has been made to observe the effect of flatness parameter, reinforcement, viscoelasticity and porosity on the phase velocity, meticulously. Some particular cases have also been discussed and it is found that velocity equation is in well-agreement to the classical Love wave equation. Moreover, some remarkable observation has been made through numerical computation and graphical demonstration for fiber-reinforced layer of carbon fiber-epoxy resin, poroelastic layer of sandstone and a viscoelastic half-space.     

Torsional stiffness of a layer bonded to an elastic half space

The static solution to the problem of a layer bonded to an elastic half-space, where the layer is driven by the torsional rotation of a bonded rigid circular disk, is considered here. An iterative solution, perturbing on that given for the elastic half-space, is obtained as a convergent power series, provided the ratio of the stratum depth to the radius of the disk is large. An equation for the applied static torque at the surface of the rigid disk is also calculated and compared, under limiting cases, with known results.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

Propagation of electro-elastic surface Love waves in a structure consisting of a piezoelectric half-space substrate of crystal class 6, 4, 6 mm or 4 mm and two layers, one of which (adjacent to the substrate) is a conducting material and the second is either a conducting or a dielectric material, is considered. The mathematical model obtained includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. Numerical calculations are carried out for three different layered structures. The effect of the second layer on the propagation behaviour of the surface Love wave in the structure is revealed.     

Rayleigh-type waves in a water-saturated porous half-space with an elastic plate on its surface

The paper deals with the plane problem of steady-state time harmonic vibrations of an infinite elastic plate resting on a water-saturated porous solid. The displacements of the plate are described by means of the linear theory of small elastic oscillations. The motion of the two-phase medium is studied within the framework of Biot's linear theory of consolidation. The main interest is focused on the investigation of properties of the Rayleigh-type waves propagating alongside of the contact surface between the plate and the porous half-space. In particular, the dependence of the phase velocity and attenuation of the waves on the plate stiffness, mass coupling coefficient, and degree of saturation of the medium is studied. Besides, for the limiting case of an infinitely thin plate, the comparison of the wave characteristics is carried out with those of the pure Rayleigh waves.     

Love waves in a layer on a regularly laminated half-space

We theoretically study the existence conditions for Love waves in a layer with arbitrary thickness and arbitrary physical and mechanical properties on a regularly laminated half-space. Also we analyze the behavior of the dispersion curves depending on the physical and geometrical properties of the layer and the mechanical properties of the upper layer of the half-space. It is demonstrated that the behavior of the spectrum and the ranges of surface waves can efficiently be controlled by varying the thickness of the layer.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 131–136, September 2004.     

Seismic Reflection from an Interface Between an Elastic Solid and a Fractured Porous Medium with Partial Saturation

The theory of Tuncay and Corapcioglu (Transp Porous Media 23:237–258, 1996a) has been employed to investigate the possibility of plane wave propagation in a fractured porous medium containing two immiscible fluids. Solid phase of the porous medium is assumed to be linearly elastic, isotropic and the fractures are assumed to be distributed isotropically throughout the medium. It has been shown that there can exist four compressional waves and one rotational wave. The phase speeds of these waves are found to be affected by the presence of fractures, in general. Of the four compressional waves, one arises due to the presence of fractures in the medium and the remaining three are those encountered by Tuncay and Corapcioglu (J Appl Mech 64:313–319, 1997). Reflection and transmission phenomena at a plane interface between a uniform elastic half-space and a fractured porous half-space containing two immiscible fluids, are analyzed due to incidence of plane longitudinal/transverse wave from uniform elastic half-space. Variation of modulus of amplitude and energy ratios with the angle of incidence are computed numerically by taking the elastic half-space as granite and the fractured porous half-space as sandstone material containing non-viscous wetting and non-wetting fluid phases. The results obtained in case of porous half-space with fractures, are compared graphically with those in case of porous half-space without fractures. It is found that the presence of fractures in the porous half-space do affect the reflection/transmission of waves, which is responsible for raising the reflection and lowering the transmission coefficients.     

On SH waves in a pre-stressed layered half-space for an incompressible elastic material

The propagation of Love waves along the boundary between a half-space and a layer of different pre-stressed material is examined for incompressible isotropic elastic materials. The secular equation is obtained for a general strain-energy function and analysed for particular deformations and materials. For the neo-Hookean strain-energy function, numerical results are obtained to illustrate the dependence of the wavespeed on the wave number and on the deformation.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.